Introduction

In any material system, the answer to what is the exciton configuration and whether exciton self-trapping occurs, deals with the intimate nature of the aggregation state and its coupling with the electronic excitations. This aspect becomes particularly relevant when one faces the task of describing the radiation–matter interactions able to produce functional modifications in materials with wide technological spread, such as silicon dioxide. Despite its consolidated role in contemporary pillar technologies, SiO2 is continuing to stimulate fundamental1,2,3 and applied studies in microelectronics4 and photonics5,6 and to generate new cutting-edge scientific fields, such as optical 5D information storage7, nanowire sensing8 and ultra-strong nanofibres9. Fundamentally, many consolidated and emerging applications of SiO2 involve radiation–matter interactions, either in the material processing or in its operative conditions. For example, above-gap excitation of SiO2 can lead to structural changes and to modifications of the optical and the dielectric response, which have an impact in fibre optics and photonics10, microelectronics11 and even in nuclear waste management12. For this reason, several studies have investigated the mechanisms of radiation-induced defect formation in SiO213, revealing their relation to exciton decay via bond dissociation or via the formation of vacancy-interstitial sites14. Nevertheless, the configuration of the SiO2 exciton is not understood in all its decay steps and current knowledge is still mostly based on paradigmatic pioneering experiments of X-ray-excited optically detected magnetic resonance in quartz15 and parallel measurements of transient optical absorption, density change and light emission by electron-beam irradiation16,17. Such experiments, supported by coeval calculations and more recent molecular dynamics studies18,19,20,21, indicate that the SiO2 exciton manifests itself in a self-trapped exciton (STE) configuration22,23, whose formation includes two main players: a three-fold coordinated silicon atom, an oxygen atom displaced from the regular coordination site and a neighbouring oxygen centre with which it forms an unspecified chemical bond. More detailed models of the STE configuration invoke the formation of a peroxy linkage13,15 or a bond between a non-bridging-oxygen (NBO) and a nearby bridging oxygen, as supported by spectroscopic studies of band-to-band excited luminescence24.

The luminescence spectrum is arguably one of the main sources of experimental information on the exciton decay in SiO2, together with parallel studies with different spectroscopic techniques25. From these evidences, the blue-green spectral region was recognized as the region of the STE light emission, mainly characterized by long lifetime resulting from the triplet state (few μs at 300 K and about 1 ms at cryogenic temperatures25,26) and excitation in the intrinsic band-to-band region. In fact, X-ray-, electron-beam-17,24,26 and two-photon-excited photoluminescence spectra26, typically show red and green-blue emissions in silica and green-blue luminescence in quartz. The green-blue component at 2.4–2.7 eV is commonly ascribed to STE and shares the spectral region with defect-related contributions of hydrogen- or alkali-decorated NBOs26,27 and oxygen-deficient centres28. These defect-related emissions possess quite long lifetimes, similarly to the STE, and in some conditions with very similar values, from 8 to 12 μs at 300 K and few 101 μs at 90 K for hydrogen-perturbed NBOs26 to about 10 ms, 112 μs and 10 μs for oxygen-deficient twofold coordinated Si, Ge and Sn sites in amorphous SiO2, respectively, at 300 K29. The red photoluminescence at 1.9 eV is, instead, associated with NBOs, which are amongst the most investigated point defects in silica30,31, with main excitation channels at 2.0 eV, 4.8 eV and 6.8 eV and relatively long lifetime of about 10–20 μs32,33,34. Variants with slightly different spectral features due to interactions with nearby functional groups26,27 or bridging35 and non-bridging oxygens36 are also commonly observed. Despite the fundamental role of elementary NBO point defects in bond-breaking events in SiO2, their red photoluminescence has never been observed in quartz, except for locally amorphized crystals by neutron irradiation37,38. Mainly for this reason, early interpretations of the band-to-band excited photoluminescence spectra did not explicitly consider the NBO emission as a possible contribution to the radiative decay of STEs.

Aim of the present work is to obtain a definite spectral insight into the relationship between NBO and STE, so as to face an unresolved critical point. In fact, despite NBOs are expected to be involved in the STE configuration, whose acknowledged spectral fingerprint is in the blue-green region, the light emission of NBO instead lies in the red and is usually ascribed to stable defects only. Here, by using synchrotron light band-to-band excited photoluminescence experiments conducted over a wide range of temperatures on a comprehensive set of silica specimens obtained through different synthetic methods and treatment conditions, as well as on pristine and neutron-irradiated quartz, we reveal that the band-to-band excited green and red luminescence in silica are not independent transitions, but instead arise from the bifurcation of the decay process of intrinsic excitations into a dual relaxation route involving either ‘free’ or ‘interacting’ NBO configurations. By doing so, our data suggest an explanation for the absence of the red luminescence in untreated quartz and a general relationship between exciton trapping and structural disorder in SiO2.

Results

Rationale of the experiments

We investigated a set of silica and quartz specimens rationally selected so as to represent the largest variety of SiO2-based materials currently known (see details in Methods). Such comparative approach is strategic for two main reasons: First, it enables us to distinguish the spectral signatures of the STE decay from different sample-dependent photoluminescence contributions. Second, it identifies the silica variant for which the temperature-controlled photoluminescence is free from non-radiative decay processes, and thus directly unveil the configurational relaxation path of band-to-band excitations. The rationale of the study is depicted in Fig. 1, while Table 1 reports the list and description of the main silica variants considered in the investigation (data on optical absorption and Raman spectra of the full set of samples are reported in Supplementary Figure 1 and Supplementary Table 1).

Fig. 1
figure 1

Rationale of the study. a Schematic depiction of the amorphous network of representative silica systems across the continuum of different structural SiO2 variants, namely the open network by sol-gel synthesis route (open) and the dense packaging of tetrahedral units in fused dry synthetic systems by chemical vapour deposition from SiCl4 (dense). b Schematic depiction of the doped network with heterogeneous dopants substituting for Si (doped), and the defective network resulting from neutron irradiation or incorporation of modifier ions/molecules (defective); silicon atoms are pictured in grey, oxygen atoms in red and heterogeneous dopants in orange). c Schematic picture of the decay channels for the band-to-band excited SiO2, showing the role of non-radiative decay processes and defects. d Radiative decay channels responsible for band-to-band excited photoluminescence when non-radiative decay channels are minimized, highlighting two ubiquitous intrinsic radiative exciton decay channels with emissions in the red and green spectral regions. The study of the radiative decay paths in a SiO2 system with suppressed non-radiative decay, and the analysis of structure-dependent exciton features in the reflectivity spectra answers longstanding questions on e, the structural configuration responsible for the radiative decay of self-trapped-exciton, f the elusive nature of NBO in crystalline SiO2 (quartz), g the intimate connection between the material structure and the excitonic spectral features

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Table 1 Silica variants. Main categories of investigated silica systems, identified by production method (first column) and perturbation level of the structural network, from nominally pure parent samples (second column) to samples conditioned by doping (third column) or by treatment-induced defects (forth column)
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As regards the use of synchrotron light (energy density < 0.1 J cm−2 and power density < 0.1 W cm−2), such an excitation source is particularly suitable for band-to-band spectroscopy. It removes difficulties that affect studies of the SiO2 exciton using other types of excitation. First, as far as the photon energy does not exceed two times the band gap, it prevents mechanisms of multiplication of electronic excitations39. Second, synchrotron radiation does not introduce structural perturbations that are instead promoted by exposure to high energy ionizing radiation and particle beams or to intense laser light40. While the excitation-induced defect generation cannot, however, be excluded completely, at least in an unstable form41, the data we present in the next sections in fact confirms that the influence of generated defects is negligible in our experiments.

Synchrotron-excited photoluminescence

In Fig. 2a we report the photoluminescence contour plots at 8 K of four silica variants (namely, p-spr, d-spr, p-cvd and s-spr) as a function of the band-to-band excitation energy, compared with the patterns excited in the sub-band-gap vacuum ultraviolet (VUV) range, which exemplify the variety of optical responses encountered in our study. Sub-band-gap VUV-excited spectra is dominated by defect-related emissions with excitation bands in the 6.5–8 eV region, ascribable to high excited states of oxygen-deficient centres (ODC) and NBO, with main emissions in the region 2.5–3.2 eV and at 1.9 eV13,27,28,29,30,31,32,34. This sub-band-gap VUV-excited response is consistent with previous data, mainly showing ODC luminescence excited at about 5 eV, specifically in Sn-doped silica29,42, Ge-doped silica29,42,43, Si-rich silica29,44 and silica from chemical vapour deposition (CVD)45, either treated and untreated. By contrast, notwithstanding the large structural/compositional differences between the investigated material systems, Fig. 2a reveals a ubiquitous pattern excited above gap, with two spectral contributions always paired to each other and without a reliable relationship with the intensity of sub-band gap excited defect-related emissions: one at ~2.5 eV corresponding to the STE photoluminescence and one at ~1.9 eV ascribable to NBO-like emission. This fact strongly suggests that these emissions are caused by intrinsic decay paths of interband excitations. We note that similar red and green components are also observed in fractoluminescence spectra of silica46, where the double emission is strictly related to intrinsic bond-breaking processes. However, the data in Fig. 2a rule out any strong contribution by defects that in principle could give rise to similar emissions, such as native NBOs and ODCs. In fact, within the investigated materials, the intensity ratio between band-to-band excited and sub-band-gap excited green and red luminescence includes values larger than 1. This outcome is inconsistent with an attribution to defects only, because the excited volume at 10 eV is much smaller (of the order of 10–8 cm3 if the absorption coefficient is 105 cm−1)47,48 than in the spectral region 5–7 eV (of the order of 10–5 cm3 with an absorption coefficient of few 102 cm−1)49,50,51. Therefore, the number of defects that can be directly excited by above-gap one-photon absorption is three orders of magnitude smaller than the number of defects excited below gap. Such a difference cannot be compensated by the different excitation yield in the two spectral regions, since the energy deposited per absorbed photon in our experiments (100–101 eV) and the absorption events per unit time (108–109 photons ms−1) are not expected to provide much more than one secondarily excited defect per absorbed photon. The collected spectra also confirm that above-band-gap excitation does not significantly excite luminescence from surface-related defects such as those observed on porous silica52. The excited volume is much thicker than the surface reconstruction layer, and a factor 101–102 greater than the thinner SiO2 films that were proved to give a bulk response48. We indeed estimate (on the basis of VUV absorption and reflectivity data49,50,51), a radiation attenuation depth in the region 8.5–17 eV ranging from 20 to 200 nm, which correspond to about 102–103 layers of coordination units.

Fig. 2
figure 2

Band-to-band excitation-emission spectra. a Contour plots of light emission spectra at 8 K excited above the band gap energy from 9 to 17 eV and in the sub-band-gap VUV region from 6.3 to 9 eV in fully densified pure sol-gel silica (u-spr), in sol-gel silica synthesized by addition of 1 mol% of Si2(OCH3)6 as a molecular precursor of Si–Si groups defectiveness (d-spr), in pure synthetic commercial dry silica by chemical vapour deposition (u-cvd), and in fully densified sol-gel silica doped with 0.2 mol% SnO2 (s-spr); dashed lines are guides for the eye. b Comparison between photoluminescence spectra (experimental data in grey, smoothed data in full line) excited at 13.8 eV at 8 K and 300 K in u-cvd, in the same material after neutron irradiation at a fluence of 1018 neutrons per cm2 (n-cvd), in d-spr, in s-spr, in u-spr and in pure synthetic commercial dry silica by chemical vapour deposition with 2 mol% GeO2 (g-cvd). Additional blue-violet component at 2.7–3.1 eV at 300 K is caused by thermally activated transitions at intrinsic or extrinsic ODCs

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Figure 2b and Supplementary Figure 2 show photoluminescence spectra of all investigated silica variants at 8 K and at room temperature, highlighting the common behaviour across the sample set. Despite the structural/compositional differences, all materials exhibit a similar evolution of their emission spectrum with temperature, showing strong red luminescence at cryogenic temperature that becomes dominated by a green emission at room temperature, disregarding of the absolute thermal quenching of the total intensity.

Deeper details of the temperature effects emerge from Fig. 3. Figure 3a displays the integrated intensity of the red and the green emission bands as a function of temperature, extracted from the respective photoluminescence spectra as shown in Fig. 3b. We notice that, while thermally activated processes cause an essentially monotonic dimming of the red emission in all the investigated systems (fluctuations are within the experimental uncertainty), the green component in most samples (u-cvd, u-spr, g-cvd and n-cvd in Fig. 3a) shows a markedly non-monotonic behaviour, comprising a gradual decrease with the temperature approaching room conditions. This indicates the occurrence of sample-dependent thermally activated non-radiative mechanisms competing also with the green emission channel. This points to a role of coordination defects, which vary from sample to sample, as non-radiative traps for the silica exciton41. Accordingly, except for minor fluctuations, the defective d-spr Si-enriched material shows the green emission with a basically monotonic negative trend with increasing temperature. Importantly, parallel to this feature, green emission and red emission too are known to have negligible thermal dependence of the decay kinetics53. Such a feature points to sample-dependent quenching mechanisms that are not caused by competitive decay paths in the emitting system itself, but to factors which influence the number of emitting sites, either before the formation of the excited state or after the radiative transition. Post-transition events were suggested to be the cause of thermal quenching of sub-band-gap excited green emission through the annihilation of transient centres produced by optical excitation53. Band-to-band excitations present a quite different scenario, since the photon energies are not generally resonant with localized defect transitions, but generate instead free electrons, holes and excitons. In that case, pre-transition events must be taken into account as a source of processes competitive with the radiative decay of the excitation. These processes must generally include the migration of the excitation that eventually results in electron/hole localization in traps, defect formation or thermalization at defect sites.

Fig. 3
figure 3

Effects of competitive non-radiative decay. a Integrated intensity of the red and the green photoluminescence (red and green circles, respectively) excited at 13.8 eV as a function of temperature (8–300 K) for different silica systems (from left to right, starting from the top, pure synthetic commercial dry silica by chemical vapour deposition (u-cvd), fully densified pure sol-gel silica (u-spr), synthetic commercial dry silica by chemical vapour deposition with 2 mol% GeO2 (g-cvd), u-cvd material after neutron irradiation at a fluence of 1018 neutrons per cm2 (n-cvd), sol-gel silica synthesized by addition of 1 mol% of Si2(OCH3)6 as a molecular precursor of Si–Si groups defectiveness (d-spr), and fully densified sol-gel silica doped with 0.2 mol% SnO2 (s-spr)). The uncertainty, estimated from the integrated noise-to-signal ratios of each spectrum, is reported as error bars for each experimental value. b Spectral ranges (indicated by red and green filled areas in a representative photoluminescence spectrum) used for the extraction of the integrated intensity data reported in a upon renormalization to the integrated intensity of the total photoluminescence spectrum at 8 K. c Relationship between the temperature dependency rates (dIPL/dT) of the red and the green emissions (circles at negative and positive values, respectively) extracted from a for s-spr (highlighted by grey-shaded background); the uncertainty propagated from the noise-to-signal in IPL data is reported as error bars. The linear regression of the data sets is reported as solid red and green lines. The dashed line indicates the slope ratio, which is nearly constant across the whole temperature range

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In fact, if on the one hand there are many studies which clarify the occurrence of exciton self-trapping in SiO225, on the other hand there are also evidences of excitation migration in the amorphous network24,52,53,54,55, as well as theoretical basis for a non-null energy barrier and delay for exciton self-trapping in amorphous SiO221,22,56,57. The available data indeed points to a non-null delay for exciton self-trapping in SiO254, and to an excitation diffusion length for the self-trapped exciton too (via hopping migration) of the order of 101 nm24. Noteworthy, the mobile nature of excitation in SiO2 is also consistent with the analysis of the spectral shape of the exciton absorption peak at 10.2 eV58. Accordingly, the progressive drop of the total photoluminescence efficiency in all systems (blue symbols in Fig. 3a), except for the s-spr material (highlighted by grey shading) that is discussed in the next section, points to a non-negligible role of thermally assisted exciton migration towards non-radiative trapping sites competing with the radiative decay.

A single origin for the red and green photoluminescence

In contrast to the silica systems discussed in the previous section, showing a drop of both their red and green emission bands with increasing temperature41, a strict anti-correlation between the two photoluminescence intensities is found for the s-spr material (Fig. 3a, c), which is unprecedented in the literature. Notably, the total spectrally integrated photoluminescence intensity is nearly temperature independent, compared with the other systems, and the thermal rates of the green and red emission intensity differ from each other only for a constant scale factor (about −1.5) (Fig. 3c). These data suggest a decay kinetics in which the two emissions are not independent of each other, arising instead from the same kind of configuration undergoing one of two competitive transitions anticorrelated by some kind of intersystem crossing process. This interpretation is confirmed by the thermal evolution of the photoluminescence spectrum of the s-spr material in Fig. 4a that, being only weakly affected by non-radiative decay losses (note the weak ~20% dimming of the spectrally integrated intensity between 8 and 300 K in Fig. 4b), provides direct insight into the local relaxation process of the STE. As a result of the suppression of quenching effects, the spectra vs. temperature in Fig. 4a reveal a clear-cut isostilbic point at 2.0 eV, where the photoluminescence intensity is constant at any temperature (Fig. 4c), despite the progressive shift of the spectral distribution of the emitted photons from the red band to the green component (Fig. 4b).

Fig. 4
figure 4

Interconversion between red and green emissions. a Photoluminescence spectra excited at 13.8 eV, collected at different temperature from 8 to 300 K (from blue to red) in s-spr silica, showing an isostilbic point at 2.0 eV where photoluminescence intensity is independent of the temperature-induced changes of red and green components. b Integrated counts I of the emissions from α (red circles) or β (green circles) states, and their sum (blue circles) in s-spr sample; the uncertainty, estimated from the integrated noise-to-signal ratios of each spectrum, is reported as error bars for each experimental value; curves are fits of the data following the model described in the text with ktnr/ktrad = Kexp(−Enr/kBT), with K = 0.79 ± 0.18 and Enr = 12 ± 3 meV, and kisc/kα = K0exp(−Eisc/kBT), with K0 = 6.5 ± 2.3 and Eisc = 16 ± 3 meV of activation energy for STE transition to β-state. c Temperature dependence of the photoluminescence intensity Iiso at the isostilbic point energy 2.0 eV, normalized to the low temperature value; the uncertainty, estimated from the integrated noise-to-signal ratios of each spectrum, is reported as error bars for each experimental value. d Spectra collected at different temperature from 8 to 300 K (from blue to red) on the same sample by exciting at 210 nm, below the energy gap. e Schematics of energy levels with radiative (continuous arrows) and non-radiative (dashed arrows) transitions involved in STE decay and subsequent relaxation to α or β excited levels responsible for red and green emissions, respectively; Kinetic rates are indicated as in the text. f Representative experimental or theoretical photoluminescence spectra of NBO variants including: free NBO30, NBOs on crystal surfaces (cry-SiO2)36, and alkali-perturbed NBOs27. g Photoluminescence spectra excited at 13.8 eV of pure synthetic quartz (p-q) at 8 K (blue curve) and 300 K (red curve). h Photoluminescence spectra excited at 13.8 eV of pure synthetic quartz after neutron irradiation (n-q) at 8 K (blue curve) and 300 K (red curve)

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Importantly, sub-band-gap excited spectra do not show an isostilbic point (Fig. 4d). In this case, the spectra are dominated by the emission of NBO and Sn-variant of ODC at 1.9 eV and 3.1 eV42, respectively, with intensity decreasing at increasing temperature. An isostilbic point has non-zero probability to occur only when the luminescence spectrum arises from two states connected to each other by an interconversion process (see Supplementary Note 1)59,60. Therefore, data in Fig. 4a reveal, for the first time, a common configurational origin of the two decay channels and identify a twofold relaxation process as local STE decay mechanism in SiO2. The isostilbic point in Fig. 4a is also an indirect demonstration that radiation-induced NBOs, if any, do not contribute significantly to the emission spectra upon above-band-gap excitation, since they would otherwise give a spectral contribution at 1.9 eV uncorrelated with the 2.5 eV emission, inconsistently with the occurrence of an isostilbic point which instead highlights a pure intersystem crossing process. The energy scheme of the electronic states involved in such a thermally activated conversion process is sketched in Fig. 4e. According to this scheme, a photogenerated exciton is originally self-trapped into a ‘free NBO’ configuration (α state) that either decays radiatively by emitting a 1.9 eV photon (with rate kα) or undergoes thermally assisted intersystem crossing (with rate kISC) to a slightly modified configuration (β), from which the green emission at 2.5 eV occurs with rate kβ. The moderate non-radiative effects responsible for the weak photoluminescence dimming with increasing temperature is accounted for by a competitive pathway, common to both the decay channels. We assign to this effect a rate knr = Kexp[−Eb/kBT] that can be determined from the spectrally integrated photoluminescence intensity vs. T in Fig. 4b. This effect is mainly driven by trapping in non-radiative defects occurring before exciton localization in the radiative sites, as discussed in the next section. Accordingly, thermally activated multi-phonon non-radiative channels competitive to radiative decay are expected to be negligible, as previously inferred25,33. Within these assumptions, the intensity (IR,G) of the red and the green emission can be expressed through the equation IR,G = C/{1 + (K0exp[−Eisc/kBT])n}, where K0 = kISC(T = ∞)/kα, Eisc is the activation energy of the intersystem crossing process and C = ktrad/[ktrad + ktnr], where ktrad and ktnr are, respectively, the radiative and non-radiative decay rate of trapped excitons. The exponent n is 1 for the red emission and –1 for the green band.

By using this model to fit the experimental data in Fig. 4b, we obtain an activation energy E = 16 ± 3 meV, which is reasonably close to the recently discovered low-energy phonon mode (8 meV)37 coupled to NBOs in SiO2. This suggests that the inter-configurational α → β conversion process might be promoted by a low-energy vibration, such as a NBO bending mode enhancing the interaction between a NBO and its surrounding atoms and thereby stabilizing the perturbed electronic density of the non-bridging moiety. Following this argument, the 1.9 eV and the 2.5 eV emissions seem to be ascribable to two NBO configurational variants. Accordingly, the green band is peaked at 2.5 eV, which is consistent with the emission energy of NBOs perturbed by the interaction with nearby groups27,36. In Fig. 4f, we summarize the emission spectra, determined either experimentally or theoretically, for different NBO variants, including the ‘free NBO’ species reported in the original work by Skuja30 and the NBOs perturbed by the interaction with nearby alkali ions found by Zatsepin et al.27 in alkali-silicate glasses, which show progressively lower emission energy from 2.6 eV to 2.4 eV in the sequence Li → Na → K, according to the lower ionic field strength of cations with larger ionic radius. Accordingly, theoretical calculations on different types of SiO2 surfaces predicted larger transition energies for NBO groups interacting with nearby bridging oxygen atoms36.

The observation of the red-emitting and green-emitting STEs being ‘unperturbed’ or ‘structurally perturbed’ variants of the same NBO centre has important consequences on our understanding of the optical behaviour of crystalline SiO2. Specifically, it explains why the red emission from ‘non-interacting’ NBOs has never been observed in quartz, while it is commonly exhibited by amorphous or amorphized SiO2 materials. The more compact structure of quartz with respect to the open network of amorphous silica promotes the interaction between NBOs and their surrounding lattice. As a result, exciton decay occurs exclusively through interacting NBOs, leading to the typical green luminescence band and no red emission by isolated NBOs. To verify this point, in Fig. 4g, h, we also report the band-to-band excited photoluminescence spectra of pure synthetic quartz, respectively before (sample p-q) and after (sample n-q) neutron irradiation. In agreement with the above interpretation, the pristine material exhibits photoluminescence in the green spectral region at 2.5–2.7 eV. On the other hand, upon partial amorphization by heavy neutron irradiation (at a fluence of 1018 cm−2)36, the low temperature photoluminescence spectrum becomes dominated by a 1.6–1.8 eV red emission band compatible with the radiative decay of non-interacting NBOs, completely quenched at room temperature.

Radiative vs. non-radiative exciton decay

A further compelling consequence of the unique photophysical behaviour of the s-spr material in Figs. 2 and 3 is a potential strategy for designing SiO2 networks with intrinsic excitations nearly unaffected by thermally assisted decay in non-radiative defects. Two possible factors could cause the insensitivity to thermal photoluminescence quenching of the s-spr system: (i) a low density of non-radiative defects and (ii) the occurrence of strongly competitive mechanisms of radiative decay in regular sites, absent in other SiO2 variants, promoted by local perturbations caused by substitution of regular Si sites by Sn atoms. Such dopant-related effect would enhance the exciton localization without preventing excitons from recombining radiatively. Figure 5a shows a schematic depiction of this latter scenario. Figure 5b depicts the situation in a highly defective network without preferential paths for radiative recombination in alternative decay sites.

Fig. 5
figure 5

Exciton trapping paths. a Schematics 2D representation of an amorphous network (points connected by sticks) with a concentration of non-radiative defects (red diamonds) lower than the concentration of substituted sites characterized by large trapping cross section and high rate of radiative recombination (grey circles). Rs and Rd are the mean distances an exciton (at the centre) has to travel before finding substituted sites or defects, respectively. b Representation of an opposite situation of a network with large defectiveness and no site of preferential trapping and radiative decay. Rm represents the mean free path of exciton in the unperturbed network. In s-spr material, the calculated Rs and Rd values are about 5 and 9 nm, respectively, while Rm in SiO2 was estimated to range from 30 to 300 nm26. c Temperature dependence of the quantum yield ηrad at different ratios between radiative and non-radiative traps, in the case of trap density nsrad + ndeft = 0.1 mol%, Δε/kB = 70 K, and σtraps = 70σirad, with Δεsrad = Δεdef = Δε σsrad = σdef = σtraps

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Both such situations can be described by a photoluminescence quantum efficiency, ηr = (kirad + ksrad)/(kirad + ksrad + kdef), determined by three exciton decay rates, respectively in intrinsic radiative sites (kirad), substituted radiative sites (ksrad) and non-radiative defects (kdef), each of which assumes different values depending on the relative concentration of the respective sites. Specifically, the different rates, kj with j = irad, srad, def, can be expressed as kj = njνjdσj, where νj and d are respectively the frequency and the step length of the exciton hopping process and nj and σj are the number density and cross section of the j-th type of site. The term, νj = ν0exp[−(εj − ε0)/kBT] accounts for the thermally activated hopping from a regular site (with energy ε0) to an adjacent perturbed site (with energy εj), resulting in non-nil activation energy Δεj = εj − ε0 for hopping in perturbed sites. In turn, nj∼Rj−3 where Rj is the mean distance between neighbouring sites, as sketched in Fig. 5a, b.

This approach yields a temperature-dependent photoluminescence quantum yield ηr(T) = (1 + Sae−Δε/kT)/(1 + ae−Δε/kT), where S = nsrad/(nsrad + ndef) expresses the balance between the relative abundance of substituted radiative and non-radiative decay sites sampled by an exciton. For concentration of non-radiative decay sites much lower than radiative ones, corresponding to S∼1, the expression describes a situation of nearly T-independent ηr. On the other hand, for larger fractions of non-radiative sites (S∼0), ηr experiences severe temperature quenching. These scenarios are exemplified in Fig. 5c, where the total concentration (nsrad + ndef) of radiative and non-radiative perturbed sites is kept constant at 0.1 mol% of the total intrinsic network sites, whereas the other parameters are adjusted to reproduce the strongly thermally quenched behaviour of the heavily defective undoped material (e.g. n-cvd in Fig. 3a). Interestingly, by comparing Fig. 5c with the weak thermal dependence of the total emission intensity of the s-spr material in Fig. 4c, we find that the concentration of radiative decay sites must be just below S = 1 (~0.7–0.8), which is compatible with the expected concentration of regularly coordinated Sn-substituted sites (see below).

The experimental data on s-spr material shown in Fig. 4 are compatible with the situation depicted in Fig. 5a, where thermally activated exciton decay in non-radiative sites plays a negligible role with respect to localization in radiative centres. In order to experimentally validate this interpretation, we combine the optical absorption spectra of coordination defects in the near-UV with reflectivity spectra in the spectral region of the excitonic peak. We note that the relatively low density of non-radiative defects in s-spr material from the analysis in Fig. 5 suggests that Sn-doping does not relevantly increase the defect concentration, particularly twofold coordinated defects. Accordingly, the s-spr material shows a relatively small absorption coefficient of ~3 cm−1 at 5 eV (Supplementary Figure 1), corresponding to twofold coordinated defects with concentration of ~ 101 ppm (considering an oscillator strength f = 10–1)28. This ‘lattice curing’ effect is typical of dopants introduced during sol-gel synthesis, where the occurrence of coordination defects at cation sites is strongly reduced with respect to CVD processes40,42, as in Ge-doped sol-gel silica61. As a result, in the s-spr material, the concentration of non-radiative cationic defects is approximately an order of magnitude smaller than Sn sites and S~ 1. Considering a 1 nm3 cell containing 24 cations (consistently with density of silica20,21), the resulting distance between two neighbouring Sn sites is less than six steps in the cation sublattice, which makes exciton localization in non-radiative defects statistically less probable with respect to localization in Sn-substituted sites. The analysis of the excitonic peak in the reflectivity spectra further indicates that Sn-substituted sites have a significantly larger cross section with respect to the intrinsic sites, which enhances their ability to act as localization sites for radiative decay with respect to exciton migration to non-radiative traps.

Reflectivity spectra and exciton bandwidth

Efficient exciton localization at Sn sites is expected to involve relevant fluctuations of the local potential, which should result in a measurable broadening of the excitonic reflectivity peak. The comparison between reflectivity spectra of the silica variants, including data extracted from the literature58,62,63,64, is reported in Fig. 6a. We fitted the reflectivity profiles starting from the real and imaginary parts of the dielectric function ε(E), which we described through the superposition of a fixed number of Lorentzian contributions strictly corresponding to recognizable features in the reflectivity spectra (Fig. 6b, Supplementary Note 2 and Supplementary Table 2)65. Notably, the model reproduces the exciton peak at ~10 eV in all investigated cases with a lorentzian function (solid curves in Fig. 6a), consistently with the assumption of exciton migration66. Fundamentally for our discussion, the spectral position, Eexc and linewidth, Γ, values of the excitonic reflectivity peak are spread between 10.15–10.45 eV and 0.20–0.27 eV, respectively, which is likely the result of different fluctuations of the local potential between the various silica systems.

Fig. 6
figure 6

Reflectivity spectra. a Reflectivity spectra (points) of different silica samples: from back to front, in sol-gel silica synthesized by addition of 1 mol% of Si2(OCH3)6 as a molecular precursor of Si–Si groups defectiveness (d-spr), pure synthetic commercial dry silica by chemical vapour deposition after neutron irradiation at a fluence of 1018 neutrons per cm2 (n-cvd), fully densified sol-gel silica doped with 0.2 mol% SnO2 (s-spr), fully densified pure sol-gel silica (u-spr), and pure synthetic commercial dry silica by chemical vapour deposition (u-cvd); fit of the experimental data by means of the expression of the reflectivity R as a function of real and imaginary parts of the complex dielectric function ε(E) are shown by solid lines. b Imaginary (left side panel) and real (right side panel) parts of ε(E) (curves on the left and on the right, respectively), obtained as sum of Lorentzian components with spectral position and width extracted from the fit of the reflectivity data in a. Data from literature (Philipp) are also reported for comparison. c Spectral bandwidth, ΓL, as a function of the respective peak position energy of the exciton component at ~10.3 eV (peaks in red in Im(ε) in b). Values obtained from literature reports are also reported and labelled by the first author’s name of the respective study. The dashed lines indicate the result of the linear regression of the data. The shadowed areas are the regions of confidence corresponding to 2σ and 3σ deviations. The same colour code applies throughout the figure

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Importantly, by plotting the values of Γ as a function of Eexc (Fig. 6c), we find that the two parameters are inversely proportional to each other in a seemingly general linear relationship. This result resembles the observation of the mutual relationship between Γ and Eexc as a function of the temperature by Schreiber and Toyozawa66, who found that Γ and Eexc are both determined by the thermal activation of lattice vibrations (dynamic response). The resulting temperature dependence is expressed through the equations, Γ(T) = Γ0 + γTn and Eexc(T) = E0–εT, where n is an exponent close to unity (ranging from 1 to 1.5 as a function of decreasing temperature) and Γ0 and E0 are temperature-independent contributions to the two quantities. On the other hand, when comparing materials with different structure or composition at a constant temperature as in Fig. 6c, the sample-to-sample variations of Γ and Eexc describe different ‘static’ sources of potential fluctuation within each silica network. Static disorder has been shown to influence the hole trapping process in silica67. However, to date, no similar effect has been reported for the SiO2 exciton. Analogously to the ‘dynamic’ description, we can describe the static contribution to Γ and Eexc through the temperature-independent linewidth Γ0 = Γ̃0 + γ̃Θn and peak energy E0 = Ẽ0 – ε̃Θ, where Θ is a generalized configurational temperature accounting for the structural characteristics of the different silica variants due to synthesis and treatment conditions and Γ̃0 and Ẽ0 are constants. Through this approach, the potential fluctuation due to static disorder yields a quasi-linear Θ-dependence of both Γ and Eexc. As a result, at a given temperature T, the exciton bandwidth and peak energy in structurally different SiO2 systems are mutually connected by a linear relationship Γ = −aEexc + b (with a,b > 0) where, for n = 1, a = γ̃/ε̃ corresponds to the rate (∂Γ0/∂E0) of structure-dependent broadening caused by changes in the structure-dependent shift of the exciton peak energy. In agreement with our analysis, the plot in Fig. 6c shows the general linear relationship between the exciton peak linewidth and energy, demonstrating the role of disorder in trapping excitons in silica. Notably, the theoretical curve calculated using a = 0.163 and b = 1.91 eV fits almost 90% of the data for undoped silica materials within a standard deviation of 1.6, as expected for a normal distribution.

A further, and possibly more compelling, aspect emerging from Fig. 6c is that, for the partially Sn-substituted system, where exciton decay in Sn sites is strongly favoured with respect to other network sites, both Γ and Eexc deviate by over 3σ from the linear relationship. The deviation consists in a much larger Γ (or Eexc) than expected at the observed Eexc (or Γ). Actually, substitution of Si by Sn atoms (with larger electron density) can hardly be a source of energy gap widening, rather the opposite, since SnO2 has a much narrower gap than silica, even in nanostructured materials68. Therefore, the observed deviation suggests a different source, other than the intrinsic topological disorder, of line broadening. This source is likely associated to fluctuations of the local potential at Sn sites, contributing to the amplitude, D, of lattice displacement. The parameter Γ is, indeed, proportional to D2/B, where B is a measure of the exciton energy band66. Since Sn sites are a minor fraction of the network sites, the exciton energy band is expected to be only weakly perturbed by Sn doping, with the system essentially behaving as an intrinsic network, leaving as the only effect of doping a relevant spectral broadening66. Figure 6c constitutes the first experimental confirmation of Schreiber–Toyozawa calculations of impurity effects on the excitonic spectrum in SiO269.

Discussion

The above analysis shows that, side-by-side investigations by means of synchrotron radiation excited photoluminescence and reflectivity experiments on a comprehensive collection of silica and quartz variants from different synthesis and processing conditions has enabled us to capture an unconventional perspective on generalities and peculiarities of SiO2-based systems. Specifically, in Sn-doped sol-gel silica with strongly suppressed non-radiative decay channels, we identified unprecedented fingerprints of double configuration in the interband-excited green luminescence previously ascribed to self-trapped exciton that could not be observed in other silica systems due to the dominant effect of non-radiative trapping processes. The in-depth analysis of the origin of such dual radiative response revealed a relationship between the exciton peak position and bandwidth in SiO2 systems, which are parametrically linked to each other by structural effects on the exciton mobility and trapping processes. Such relationship, validated by experimental data acquired by us and extracted from representative literature reports, provides guidelines for the future design of silica-based materials with tailored optical properties by rational engineering of the material structure, with potential applicative impact on VUV technologies. Finally, taken together, our results offer an insight into the photophysical mechanisms responsible for the apparent absence of non-bridging oxygen centres in quartz. The evidence of the interplay between free and interacting non-bridging oxygens in the radiative exciton decay process, unambiguously identifies NBO as the elementary and fundamental player in radiation-induced bond-breaking events in all known varieties of silicon dioxide, with a range of emission energies depending on the specific interaction with the nearby structural environment.

Methods

Materials

The set of investigated samples comprises silica and quartz from different sources, either commercial or synthesized in our laboratory by sol-gel methods, and with different kinds of perturbation, by post-synthesis treatments or doping processes. All samples were polished to optical grade with a final thickness between 0.2 and 1.2 mm depending on the sample. The description of the investigated samples—with the labels used in the text—with details on synthesis and/or treatment is given below. Information on structural and optical features, as we obtained by spectroscopic measurements (Supplementary Figure 1), are described in Supplementary Table 1. Sample u-cvd (undoped silica by CVD) is Tetrasil SE material purchased from Quartz & Silice, France. It is a type IV dry silica by vapour phase oxidation of SiCl4 in water-free oxygen/argon plasma torch. Sample w-cvd (wet silica by CVD) is Tetrasil B material purchased from Quartz & Silice, France. It is a type III wet silica by hydrolysis of SiCl4 sprayed into a hydrogen–oxygen flame. Sample g-cvd (Ge-doped silica by chemical vapour-deposition) is Ge-doped silica from an optical fibre preform purchased from Fibre Ottiche Sud, Italy. It is a type IV dry silica by modified chemical vapour deposition of SiCl4 and GeCl4 in oxidizing atmosphere. The germanium content is 2% mol. Sample p-q (pure quartz crystalline sample) is quartz from a Sawyer Premium Q single crystal bar prepared by hydrothermal growth. Samples were cut perpendicular to the optical axis. Samples n-q and n-cvd (neutron-irradiated samples) are obtained from p-q and u-cvd by neutron irradiation using a Triga Mark II reactor (Casaccia, Italy) with a fluence of 1018 neutrons per cm2. Sample u-spr (undoped silica by solution-processing route) is pure silica by solgel. It was obtained by preparing in a polypropylene container 12 mL of a solution of ethanol (EtOH), tetraethoxysilane (TEOS) and water70. The relative molar ratio of the precursors Si:H2O:EtOH was 1:7.4:10.7. The container was then sealed and put into a thermostatic chamber at 40 °C. The container cap was pierced so as to allow slow evaporation of the solvent. After 15 days of ageing, the obtained xerogel was sintered according to the following process: heating under oxygen atmosphere up to 105 °C (heating rate 10 °C h−1) and maintained for 4 h; heated under oxygen atmosphere up to 450 °C (heating rate 10 °C h−1) and maintained for 2 days; heated in vacuum (1.33 Pa) up to 950 °C (heating rate 4 °C h−1); heated under oxygen atmosphere up to 1050 °C (heating rate 4 °C h−1) and maintained for 20 h. Starting from this method the following modified solgel samples were prepared: Sample u2-spr (silica by solution-processing route with acetylacetone) is a variant of pure silica solgel sample by using the method described for u-spr and adding in the solution acetylacetone (acacH), with a final molar ratio Si:H2O:EtOH:acacH of 1:7.4:7.6:3. Sample d-spr (silica doped with 1% mol of Si–Si by solution-processing route) is defective silica intentionally doped with oxygen deficiency centres (ODC). It was prepared by the same method described for u-spr and adding, in the starting solution, 1% mol l of hexamethoxydisilane, a precursor containing the Si–Si group. Sample s-spr (silica doped with 0.2% mol of Sn by solution-processing route) is tin-doped solgel silica by the same method described for u-spr and adding 0.2% mol of dibtuyl tin diacetate as Sn precursor. Sample f-spr (silica doped with 2% mol of F by solution-processing route) is fluorine doped solgel silica by the same method described for u-spr and adding 2% mol of triethoxyfluorosilane as F precursor. Sample e-spr (silica doped with 0.5% mol of Er by solution-processing route) is erbium doped solgel silica by the same method described for u-spr and adding 0.5% mol of erbium (III) nitrate as Er precursor.

Measurements

Reflectivity and photoluminescence (PL) measurements were carried out in ultra-high vacuum with synchrotron radiation at the SUPERLUMI experimental station of HASYLAB at DESY (Hamburg, Germany). The incident beam spectral bandwidth was 0.3 nm, pulse width 130 ps, interpulse 192 ns. The reflected beam was collected, in near-normal geometry, by means of a photomultiplier tube coated with sodium salicylate. Raw data were then corrected and scaled so as to account for the spectral distribution of the incident beam and to match silica reflectivity in the visible spectral region. PL were measured by integrating the signal detected with a charge-coupled device (CCD) coupled with a monochromator with a bandwidth of 3 nm. Data were corrected for the spectral dependence of the excitation intensity and spectral response of emission monochromator and detector. Low temperature measurements were collected after stabilizing the temperature with an accuracy of 1 K. Excitation-induced modification of the above-band-gap excited emission spectrum by possible defect generation was checked by comparing repeated spectral scans, collecting spectra in one shot by means of a polychromator and a CCD detector. No appreciable change was observed above the noise, both for acquisition time of minutes and for shorter exposure time, down to few seconds only. Details on the spectroscopic methods used in Raman, infra-red and near UV absorption measurements are reported in Supplementary Method 1.